# Sensory Mathematics

and Mathematics

Key to Learning

Sensory Mathematics aims to develop children's ability to analyse the external, visual qualities of objects using sensory standards such as colour, shape and size. It also builds the foundation for the development of mental abilities

Mathematics uses visual models children discover the language of Mathematics and the concept of measurement, compare different quantities and qualities of objects and explore the relationships more, less and equal.

Watch the introductory video below!

## Overview

Sensory Mathematics helps children to recognise and apply fundamental sensory standards of colour, shape and size. It enables them to begin to analyse objects and their relationships using culturally defined sensory norms.

The natural world is almost overwhelmingly rich in its diversity of colours, shapes and forms. Our senses give us the ability to perceive this diversity, but it is culture that teaches us to understand our perceptions, for example, how to look and what to look at. Human cultures organise experience, systematising and classifying it in ways that allow us to make sense of the world and to operate confidently within it. Sensory abilities, shaped by our cultures, are the foundation upon which mental development builds.

## Why are these skills important?

It is common to offer young children opportunities to name colours, or shapes, or to use size vocabulary. The Sensory Mathematics programme aims to do much more than merely teach young children to attach labels to objects – that is red, that is a triangle, that is big, that is small. Practical activities encourage children to consider what it means to say that something is red, or that this object is a triangle, or that one object is bigger than another. Tasks focus on how we can tell one colour or one shape from another; on how we know one thing is bigger than another, but smaller than something else. Naming the sensory properties of objects is the final consolidating step in a process of exploring and internalising perceptual concepts.

## How does Sensory Mathematics work?

A particular feature of the programme is the very careful introduction of concepts of size. An object’s shape and colour are intrinsic – they do not change unless the object itself changes. Size, however, is relative, and later conventional. A cat is small in comparison with an elephant, but big in comparison with a mouse – the object has not changed but the context has. Later stages of the programme introduce the children to some of the conventional systems we use for organising perception. For example, the children learn about the colours of the spectrum; about variations of geometric shapes (right angle, acute angle and obtuse angled triangles, rectangles with differing proportions of length and width); and about the different parameters of size (length, breadth and width).

## How is Sensory Mathematics beneficial for children?

The programme embeds fundamental conceptual learning in carefully structured and sequenced everyday activities; games, stories, drawing, construction, role-play, etc. An important feature of the tasks is that they offer systematic procedures for developing understanding. These include a kinaesthetic procedure for exploring the properties of shapes, and an emphasis on systematic comparison in exploring colour and relative size. Another important feature is an emphasis on conveying that knowledge about sensory qualities is crucial. It has serious practical implications. Thus, for example, the children learn about colour by hiding mice from a dangerous cat, or about shape by feeding only appropriately shaped biscuits to each member of the shape family. There are good reasons to want to know! Last but not least, all the suggested activities have been tested in the classroom – and they are fun!

## Overview

This programme introduces the concepts and language of mathematics and develops fundamental understanding of mathematical relationships. Children discover the concept of number; they learn to think about the relationship between what is being measured and the unit of measurement required for measuring it. The main task is to help children internalise concepts of relative quantity and relative size (length, weight, volume). We aim to develop the ability to make generalisations and to see connections through the use of visual mediators.

## Why are these skills important?

Most adults accept the practical importance of mathematical skills, and in our eagerness for children to master them we are anxious to get on with the business of teaching children to count and solve number tasks. But should we begin with this? The result may be a classroom full of young children who can recite numbers up to 100, but cannot reliably count three bears. They may go through the rest of their schooling sometimes getting the right answers by following the rules, but fundamentally baffled.

A number is not a label or a digit, but the expression of a relationship between the unit of quantification and the objects or features quantified. When we look at a group of butterflies, we might count three butterflies or six wings. Similarly, when we measure the volume of water in a jug our answer depends on the measure we choose (24 tablespoons or 6 cups). By helping children grasp the underlying relationships, we help them to unlock the mystery of number.

## How does Mathematics work?

What is most distinctive about the Mathematics programme is the use of visual models to allow children to see “at a glance” the most basic but also the most fundamental mathematical relationships; more than, less than, equal to. Similarly, they learn to understand and to use simple conventional measures (e.g. a stick) to respond to scenarios in which they must compare the size of objects that cannot be gathered together in one place.

Finely graded practical activities involving a wide variety of visual mediators (pictures of objects, symbols, correspondence grids, tokens, abacuses and number lines) allow the children first to grasp and later to internalise the mathematical relationships they model. At first tasks are concretely supported. For example, children discover if there are as many carrots in a field as there are hungry rabbits by superimposing images of carrots on images of rabbits.

Gradually the tasks require greater levels of abstraction, replacing images of objects with symbols and tokens, and direct manipulation of objects with simple graphs. Later still, as the children internalise the visual models, they practise solving problems by “looking” with their “mind’s eye”.

## How is Mathematics beneficial for children?

What is really important is not quantity but quality – the quality of a child’s understanding of quantity. The secure counting and measuring skills required to facilitate mathematical learning are the apparently paradoxical outcomes of a teaching and learning process that does not focus on teaching children to count. Instead children learn to understand what they need to count and how to count it.

Children develop insight into why quantification matters; insight into the use of measures for comparing weights, heights or volumes; and the ability to focus on exactly what it is that they are trying to measure when they quantify.